CN110971558A - CAZAC sequence-based low-complexity anti-frequency offset synchronization method - Google Patents

Abstract

The invention discloses a low-complexity anti-frequency offset synchronization method based on a CAZAC sequence in a multi-carrier OFDM system, which mainly solves the problems of poor synchronization performance and high complexity of the existing algorithm, and the implementation scheme is as follows: constructing a training sequence based on a CAZAC sequence at a transmitting end; constructing a timing measurement function at a receiving end, searching the maximum value of the timing measurement function, and completing timing synchronization; and by utilizing the result of timing synchronization, estimating rough decimal frequency offset, then estimating fine decimal frequency offset, and finally estimating integral multiple frequency offset to finish frequency synchronization. The invention improves the synchronization performance of the OFDM system, simplifies the timing measurement function, reduces the calculation complexity and can be used for the wireless communication scene of burst transmission or continuous transmission.

Description

Low-complexity anti-frequency offset synchronization method based on CAZAC sequence

technical field

The invention belongs to the field of communication technologies, and in particular relates to a synchronization method for a multi-carrier OFDM system, which can be used in a wireless communication scenario of burst transmission or continuous transmission.

Background technique

As a multi-carrier modulation method, OFDM has the advantages of high spectral efficiency, resistance to frequency selective fading and easy modulation and demodulation. It has been widely used in many wireless communication scenarios, such as Long Term Evolution, LTE, Digital video broadcasting DVB, wireless local area network WLAN and so on. Although OFDM has the above advantages, its signal modulation mechanism also makes OFDM signals have some disadvantages in the transmission process, such as timing and frequency offset caused by Doppler frequency shift or oscillator instability. Sensitive, once a synchronization error occurs, the orthogonality between sub-carriers will be destroyed, and the inter-sub-carrier interference (ICI) and inter-symbol interference (ISI) will be introduced, resulting in the failure of OFDM signal demodulation. Therefore, the OFDM system has high requirements for synchronization. In recent years, many synchronization Algorithms are proposed to jointly or independently estimate timing offset and frequency offset.

In the OFDM system, the synchronization methods can be roughly divided into two categories according to whether data assistance is needed: non-data-assisted blind estimation algorithms and data-assisted estimation algorithms. in,

The non-data-aided blind estimation algorithm is generally used in continuous systems, mainly using the structural characteristics of the OFDM system itself for synchronization. Its representative algorithm is the maximum likelihood ML estimation algorithm based on cyclic prefixes, which does not require additional design of synchronization sequences. , saves the system bandwidth and improves the bandwidth utilization, but the synchronization performance is worse than that of the data-assisted algorithm.

The data-assisted estimation algorithm is generally used in burst systems, mainly using some random sequences to complete timing synchronization by capturing the peak value of the timing metric function, and then complete frequency synchronization. The random sequence is mainly composed of some sequences with good autocorrelation and cross-correlation performance, such as PN sequence or CAZAC sequence. Among them, the representative algorithms for synchronization based on PN sequences are: SC in its paper "Robust Frequency and Timing Synchronization for OFDM" (IEEE Transactions on Communications, 1997, 45: 1613-1621) proposed to use two identical sequences for The scheme of timing synchronization, but due to the existence of cyclic prefix, its timing measurement has a flat-top effect; Minn published the paper "On Timing Offset Estimation for OFDM Systems" (IEEE Communications Letters, 2000, 4: 242-244) in the SC algorithm. Based on the improvement, the four-part sequence is used for timing synchronization. Although this method eliminates the flat top effect, it still has high side lobes; Park published the paper "A Novel Timing Estimation Method for OFDM Systems" (IEEE Communications Letters , 2003, 7:53-55) designed a training sequence structure with conjugate symmetry. Compared with the SC algorithm and the Minn algorithm, the algorithm has a large peak at the correct starting point, which improves the Accuracy of timing metrics, but there are still small side lobes; Yang proposes a A coarse symbol timing algorithm based on the optimal correlation cyclic shift preamble sequence CSP, the algorithm has good performance in multipath fading channels, but its computational complexity is high.

The peak flat top effect or the existence of large side lobes in these algorithms has a certain impact on timing synchronization, and when the PN sequence is used for symbol timing synchronization, there will be a problem of peak-to-average ratio, while the CAZAC sequence has good correlation characteristics. and low peak-to-average ratio can solve these problems, so the use of CAZAC sequence for synchronization has been widely used in OFDM systems.

The existing representative algorithms for synchronization based on CAZAC sequences are: Fang in his paper "A Novel Synchronization Algorithm Based on CAZAC Sequence for OFDM Systems" (IEEE International Conference on Wireless Networks and Mobile Communications, 2012: 1-4) using random The exponential sequence weights the CAZAC sequence to complete timing synchronization. Shao published the paper "Robust Timing and Frequency Synchronization Based on Constant AmplitudeZero Autocorrelation Sequence for OFDM Systems" (IEEE International Conferenceon Communication Problem-solving, 2014:14–17) A training sequence structure similar to the Park algorithm is used in the algorithm, and the CAZAC sequence is weighted by a new weighting factor at the receiving end to complete timing synchronization. Fang algorithm and Shao algorithm perform well in multipath fading channels, but at the receiving end An additional weighted sequence needs to be used for synchronization, which wastes some storage space and at the same time increases its computational complexity; Jian published a paper "ANovel Timing Synchronization Method Based on CAZAC Sequence for OFDM Systems" (IEEE A new training sequence structure is designed in International Conference on Signal Processing, Communications and Computing, 2018: 10-15), which can reduce the computational complexity when using this structure for timing synchronization, but when there is a frequency offset, the timing of Synchronization performance drops significantly.

SUMMARY OF THE INVENTION

The purpose of the present invention is to propose a low-complexity anti-frequency offset synchronization method based on the CAZAC sequence to improve the synchronization performance and reduce the computational complexity in view of the shortcomings of the above-mentioned existing algorithms.

The technical key of the present invention is: generating a training symbol constructed by a CAZAC sequence at the transmitting end, simplifying the timing metric function at the receiving end, and utilizing the delay correlation and symmetric correlation characteristics to achieve accurate and stable synchronization, and its implementation steps include the following:

其中j为虚数单位，n＝0,1,…,N/4-1，N为OFDM系统中子载波的个数；(1) At the transmitting end, construct a training sequence based on the CAZAC sequence: T=[A(n)B(n)C(n)D(n)], where A(n) is the first part of the training sequence at the transmitting end sequence, which consists of N/4 long CAZAC sequences, denoted as

where j is an imaginary unit, n=0,1,...,N/4-1, and N is the number of subcarriers in the OFDM system;

B(n) is the second partial sequence of the training sequence at the transmitting end, which is the conjugate symmetric sequence of the A(n) sequence, that is,

C(n) is the third partial sequence of the training sequence at the transmitting end, which is obtained by inverting the even-numbered items of the A(n) sequence, that is,

D(n) is the fourth partial sequence of the training sequence at the transmitting end, which is obtained by inverting the even-numbered items of the B(n) sequence, that is,

(2) set a cyclic prefix P of length _Ng , add the cyclic prefix to the front end of the training sequence T of the transmitting end, obtain a training symbol S=[PT] with a length of N+ _Ng , and send the training symbol;

(3) At the receiving end, set the length of the receiving window as N, and construct the timing metric function M(d) within the window length:

表示相关函数，

表示能量函数，其中m，k分别为函数P(d)，R(d)的中间变量，d为采样点序号，

和

分别为数值不同的接收样本；in,

represents the correlation function,

Represents the energy function, where m and k are the intermediate variables of the functions P(d) and R(d) respectively, d is the sampling point number,

and

Respectively, the received samples with different values;

完成定时同步；(4) Search the maximum value of the timing metric function M(d) to obtain the timing synchronization estimate:

complete timing synchronization;

确定接收样本中训练序列的起点位置，得到接收端的训练序列：

其中，

为接收样本，n₁＝0,1,...,N-1，并利用该训练序列T'前后两部分序列对称的性质，计算得到粗略的小数倍频率偏移估计值

(5) According to the estimated value of timing synchronization

Determine the starting position of the training sequence in the received sample, and get the training sequence at the receiving end:

in,

In order to receive samples, n ₁ =0,1,...,N-1, and use the symmetric property of the two parts of the training sequence T' before and after the calculation to obtain a rough fractional frequency offset estimation value

确定接收样本中训练符号的起点位置，得到接收端的训练符号：

其中，

为接收样本，n₃＝-N_g,-N_g+1,...,N-1，并根据粗略的小数倍频率偏移估计值

对该训练符号S'进行粗略的小数倍频率偏移补偿，得到第一次频率偏移补偿后的训练符号S₁，再基于循环前缀进一步进行精细的小数倍频率偏移估计，计算得到精细的小数倍频率偏移估计值

(6) According to the estimated value of timing synchronization

Determine the starting position of the training symbols in the received samples, and get the training symbols at the receiving end:

in,

For the received samples, n ₃ =-N _g , -N _g +1,...,N-1, and estimate the value according to the rough fractional frequency offset

Perform a rough fractional frequency offset compensation on the training symbol S' to obtain the training symbol S ₁ after the first frequency offset compensation, and then further perform a fine fractional frequency offset estimation based on the cyclic prefix to obtain Fine fractional frequency offset estimates

对第一次频率偏移补偿后的训练符号S₁进行精细的小数倍频率偏移补偿，得到第二次频率偏移补偿后的训练符号S₂，再利用整数倍频率偏移对CAZAC序列造成移位的性质，构造整数倍频率偏移判决函数F(g)：(7) According to the fine fractional frequency offset estimate

Perform fine fractional multiple frequency offset compensation on the training symbol S ₁ after the first frequency offset compensation to obtain the training symbol S ₂ after the second frequency offset compensation, and then use the integer multiple frequency offset to perform the CAZAC sequence Due to the nature of the shift, construct an integer multiple frequency offset decision function F(g):

和

分别为两个数值不同的经过第二次频率偏移补偿后的接收样本，上标*表示取共轭；Among them, g is the independent variable of the function F(), g=0, 1, 2,..., N-1, p, q are the intermediate variables of the function F(g), respectively,

and

are two received samples with different values after the second frequency offset compensation, and the superscript * means to take the conjugate;

(8) Search for the maximum value of the integer multiple frequency offset decision function F(g), and obtain the integer multiple frequency offset estimated value:

精细的小数倍频率偏移估计值

和整数倍频率偏移估计值

得到频率偏移估计值：

完成频率同步。(9) Use a rough fractional frequency offset estimate

Fine fractional frequency offset estimates

and integer multiples of frequency offset estimates

Get the frequency offset estimate:

Complete frequency synchronization.

Compared with the existing algorithm, the present invention has the following advantages:

First, the present invention constructs a training sequence structure based on the CAZAC sequence at the transmitting end, thereby eliminating the timing metric peak plateau or large side lobe phenomenon introduced by the symmetrical structure of the cyclic prefix and the synchronization sequence itself at the receiving end, improving the performance of the training sequence. The performance of timing synchronization in Gaussian channel and multipath fading channel environment is solved, and the problems of poor timing synchronization performance and sensitivity to frequency offset of existing algorithms are solved.

Second, the present invention performs a rough fractional multiple frequency offset estimation at the receiving end first, and further performs a fine fractional multiple frequency offset estimation. This two-stage fractional multiple frequency offset correction scheme makes the frequency offset The estimation accuracy is higher, and the problem of low frequency offset estimation accuracy of the existing algorithm is solved.

Third, since all operations are performed in the time domain, the present invention does not need to undergo FFT processing, and does not need to use additional weighting sequences, which not only saves storage space, but also reduces the implementation complexity of the synchronization module, thereby improving system synchronization. speed.

Description of drawings

Fig. 1 is the realization flow chart of the present invention;

Fig. 2 is the training sequence structure diagram in the present invention;

3 is a comparison diagram of the timing detection probability of the present invention and an existing synchronization algorithm in a Gaussian channel without adding a frequency offset;

4 is a comparison diagram of the timing detection probability of the present invention and an existing synchronization algorithm in a Gaussian channel and under the condition of adding a frequency offset;

5 is a comparison diagram of the timing detection probability of the present invention and an existing synchronization algorithm in a multipath fading channel without adding a frequency offset;

Fig. 6 is the performance comparison diagram of the mean square error of frequency offset estimation of the present invention and the existing synchronization algorithm under Gaussian channel;

FIG. 7 is a comparison diagram of the mean square error performance of the frequency offset estimation of the present invention and the existing synchronization algorithm in a multipath fading channel.

Detailed ways

The embodiments and effects of the present invention will be described in further detail below with reference to the accompanying drawings.

1, the specific implementation steps of this embodiment are as follows:

Step 1, at the transmitting end, construct a training sequence T based on the CAZAC sequence.

其中j为虚数单位，n＝0,1,...,N/4-1，N为OFDM系统中子载波的个数；1a) Construct the first part sequence A(n) of the training sequence of the transmitter, which is composed of N/4 CAZAC sequences, expressed as

where j is an imaginary unit, n=0,1,...,N/4-1, and N is the number of subcarriers in the OFDM system;

其中，N₁为CAZAC序列的周期，取值为偶数，r为N₁的互质数，v＝0,1,...,N₁-1，对于A(n)序列，取r＝1，N₁＝N；Among them, the CAZAC sequence is expressed as:

Among them, N ₁ is the period of the CAZAC sequence, which is an even number, r is the co-prime number of N ₁ , v=0,1,...,N ₁ -1, for the A(n) sequence, take r=1, N ₁ =N;

1b) Construct the second partial sequence B(n) of the training sequence at the transmitting end, which is the conjugate symmetric sequence of the A(n) sequence, namely

1c) Construct the third partial sequence C(n) of the training sequence at the transmitter, which is obtained by inverting the even-numbered items of the A(n) sequence, that is,

1d) Construct the fourth part sequence D(n) of the training sequence at the transmitting end, which is obtained by inverting the even-numbered items of the B(n) sequence, that is,

1e) From the A(n) sequence, the B(n) sequence, the C(n) sequence and the D(n) sequence, the transmitter training sequence of length N is obtained: T=[A(n)B(n)C(n )D(n)], as shown in Figure 2.

Step 2, construct training symbol S.

The cyclic prefix P is formed by the N _g data signals at the end of the training sequence T at the transmitter;

The cyclic prefix P is added to the front end of the training sequence T at the transmitting end to obtain a training symbol S=[PT] with a length of N+N _g , and the training symbol is sent.

Step 3, construct the timing metric function M(d).

At the receiving end, set the length of the receiving window to be the same as the length of the training sequence T of the transmitting end, which is N, and construct the timing metric function M(d) within the length of the receiving window:

表示相关函数，

表示能量函数，其中m，k分别为函数P(d)，R(d)的中间变量，d为采样点序号，

和

分别为数值不同的接收样本。in,

represents the correlation function,

Represents the energy function, where m and k are the intermediate variables of the functions P(d) and R(d) respectively, d is the sampling point number,

and

are received samples with different values, respectively.

Step 4, complete timing synchronization.

完成定时同步。Search for the maximum value of the timing metric function M(d) to get the timing synchronization estimate:

Complete timing synchronization.

Step 5, estimate a rough fractional frequency offset

确定接收样本中训练序列的起点位置，得到接收端的训练序列：

其中，

为接收样本，n₁＝0,1,...,N-1；5a) Based on timing synchronization estimates

Determine the starting position of the training sequence in the received sample, and get the training sequence at the receiving end:

in,

For receiving samples, n ₁ =0,1,...,N-1;

5b) Using the symmetric nature of the two parts of the training sequence T' before and after, calculate a rough fractional frequency offset estimate

和

分别为两个数值不同的接收样本，n₂＝0,1,...,N/2-1，上标*表示取共轭。Among them, angle( ) represents taking the phase,

and

They are two received samples with different values, n ₂ =0, 1, .

Step 6, Estimate the fine fractional frequency offset

确定接收样本中训练符号的起点位置，得到接收端的训练符号：

其中，

为接收样本，n₃＝-N_g,-N_g+1,...,N-1；6a) Based on timing synchronization estimates

Determine the starting position of the training symbols in the received samples, and get the training symbols at the receiving end:

in,

For receiving samples, n ₃ =-N _g , -N _g +1,...,N-1;

对该训练符号S'进行粗略的小数倍频率偏移补偿，即对该训练符号S'乘以一个补偿项

得到第一次频率偏移补偿后的训练符号：

i＝0,1,...,N+N_g-1；6b) Based on rough fractional frequency offset estimates

Perform rough fractional frequency offset compensation on the training symbol S', that is, multiply the training symbol S' by a compensation term

Get the training symbols after the first frequency offset compensation:

i=0,1,...,N+ _Ng -1;

6c) Using the training symbol S ₁ after the first frequency offset compensation, based on the cyclic prefix, further perform a fine fractional multiple frequency offset estimation, and calculate a fine fractional multiple frequency offset estimation value

和

分别为两个数值不同的经过第一次频率偏移补偿后的接收样本，n₄＝0,1,...,N_g-1。in,

and

are two received samples with different values after the first frequency offset compensation, n ₄ =0, 1, . . . , N _g -1.

Step 7: Construct an integer multiple frequency offset decision function F(g).

对第一次频率偏移补偿后的训练符号S₁进行精细的小数倍频率偏移补偿，即对该训练符号S₁乘以一个补偿项

得到第二次频率偏移补偿后的训练符号：

l＝0,1,...,N+N_g-1；7a) Based on fine fractional frequency offset estimates

Perform precise fractional frequency offset compensation on the training symbol S ₁ after the first frequency offset compensation, that is, multiply the training symbol S ₁ by a compensation term

Get the training symbols after the second frequency offset compensation:

l=0,1,...,N+ _Ng -1;

7b) Using the training symbol S ₂ after the second frequency offset compensation, according to the property of shifting the CAZAC sequence caused by the integer multiple frequency offset, construct the integer multiple frequency offset decision function F(g):

和

分别为两个数值不同的经过第二次频率偏移补偿后的接收样本，上标*表示取共轭。Among them, g is the independent variable of the function F(), g=0, 1, 2,..., N-1, p, q are the intermediate variables of the function F(g), respectively,

and

They are two received samples with different values after the second frequency offset compensation, and the superscript * indicates that the conjugate is taken.

Step 8, Estimate integer frequency offset

Search for the maximum value of the integer multiple frequency offset decision function F(g) to obtain the integer multiple frequency offset estimate:

Step 9, complete frequency synchronization.

精细的小数倍频率偏移估计值

和整数倍频率偏移估计值

得到频率偏移估计值：

完成频率同步。Utilize rough fractional frequency offset estimates

Fine fractional frequency offset estimates

and integer multiples of frequency offset estimates

Get the frequency offset estimate:

Complete frequency synchronization.

The effects of the present invention will be further described below in conjunction with simulation experiments.

1. Simulation conditions:

The simulation experiment of the present invention is carried out under the MATLAB _2016B software, and the number of subcarriers in the OFDM system is set to N=256, the cyclic prefix length Ng =32, the normalized frequency offset ε=5.65 introduced, and the channels used in the simulation are respectively For the additive white Gaussian noise channel and the multipath fading channel (itur3GIBx channel in the ITU standard), the number of simulations for a single signal-to-noise ratio is set to 2000.

Existing synchronization algorithms include: SC algorithm, Minn algorithm, Park algorithm, Yang algorithm, Fang algorithm, Shao algorithm and Jian algorithm. Among them, the existing synchronization algorithms used for timing synchronization comparison include Minn algorithm, Park algorithm, Yang algorithm, Fang algorithm, Shao algorithm and Jian algorithm, and the existing synchronization algorithms used for frequency synchronization comparison include SC algorithm, Fang algorithm and Shao algorithm.

2. Simulation content and result analysis:

Simulation 1, under the above conditions, use the present invention and the above existing synchronization algorithm to perform timing synchronization in a Gaussian channel without adding frequency offset, and the result is shown in FIG. 3 . In FIG. 3 , the horizontal axis represents the signal-to-noise ratio of the OFDM system, and the unit is decibel dB, and the vertical axis represents the timing detection probability.

As can be seen from Figure 3, the present invention, Fang algorithm, Shao algorithm and Jian algorithm all have a detection probability of 1 when the signal-to-noise ratio is about 0dB, while the Park algorithm has a detection probability of 1 when the signal-to-noise ratio is about 5dB. Minn algorithm and The detection probability of the Yang algorithm can only reach 1 when the signal-to-noise ratio is about 20dB, indicating that the present invention has good timing synchronization performance in the Gaussian channel without adding frequency offset.

In simulation 2, under the above conditions, the present invention and the above-mentioned existing synchronization algorithm are used to perform timing synchronization under the condition of Gaussian channel and frequency offset, and the result is shown in FIG. 4 . In FIG. 4 , the horizontal axis represents the signal-to-noise ratio of the OFDM system, and the unit is decibel dB, and the vertical axis represents the timing detection probability.

It can be seen from Fig. 4 that when there is a frequency offset, the timing detection probability of the Jian algorithm is significantly reduced, the performance of other existing algorithms is stable, and the present invention still has good detection performance. The timing synchronization performance is good under moving conditions.

Simulation 3: Under the above conditions, the present invention and the above-mentioned existing synchronization algorithm are used to perform timing synchronization in a multipath fading channel without adding frequency offset. The result is shown in FIG. 5 . In FIG. 5 , the horizontal axis represents the signal-to-noise ratio of the OFDM system, and the unit is decibel dB, and the vertical axis represents the timing detection probability.

It can be seen from Fig. 5 that under the condition of multipath fading channel and no frequency offset, the timing detection probability of Minn algorithm, Park algorithm and Jian algorithm is obviously reduced, the performance of other existing algorithms is stable, and the present invention still has good performance. The detection performance shows that the present invention has good timing synchronization performance in the multipath fading channel without adding frequency offset.

Simulation 4, using the present invention and the above-mentioned existing synchronization algorithm to perform frequency synchronization under the Gaussian channel under the above conditions, the result is shown in FIG. 6 . In FIG. 6 , the horizontal axis represents the signal-to-noise ratio of the OFDM system, and the unit is decibel dB, and the vertical axis represents the mean square error of frequency offset estimation.

It can be seen from Fig. 6 that the mean square error performance of the frequency offset estimation of the present invention is comparable to the Fang algorithm, but better than the Shao algorithm and the SC algorithm, and with the increase of the signal-to-noise ratio, the frequency offset estimation performance of the present invention is close to the carat Merro world, it shows that the present invention has good frequency synchronization performance under Gaussian channel.

In simulation 5, under the above conditions, the present invention and the above-mentioned existing synchronization algorithm are used to perform frequency synchronization in a multipath fading channel, and the result is shown in FIG. 7 . In FIG. 7 , the horizontal axis represents the signal-to-noise ratio of the OFDM system, and the unit is decibel dB, and the vertical axis represents the mean square error of frequency offset estimation.

It can be seen from Fig. 7 that the mean square error performance of the frequency offset estimation of the present invention is comparable to the Fang algorithm, but better than the Shao algorithm and the SC algorithm, and with the increase of the signal-to-noise ratio, the frequency offset estimation performance is close to Cramer Luo Jie, it shows that the present invention has good frequency synchronization performance in multipath fading channels.

In order to compare the computational complexity of the present invention and the above-mentioned existing synchronization algorithms, the calculation amount of the present invention and the above-mentioned existing synchronization algorithms in the timing synchronization phase is calculated, and the results are shown in Table 1.

Table 1 Statistical table of calculation amount of each synchronization algorithm in timing synchronization stage

As can be seen from Table 1, in the timing synchronization stage, the number of conjugates used in the present invention is 0, the total number of complex multiplications is N+2, and the total number of additions is N-4. Compared with other algorithms , the computational complexity of the present invention is low.

Claims (7)

1. The low-complexity anti-frequency offset synchronization method based on the CAZAC sequence is characterized by comprising the following steps:

(1) at the transmitting end, a training sequence based on a CAZAC sequence is constructed: t ═ A (n), B (n), C (n) D (n)]Wherein A (N) is a first partial sequence of the training sequence of the transmitting end, which is composed of a CAZAC sequence with a length of N/4, and is represented as

J is an imaginary unit, N is 0,1, …, N/4-1, and N is the number of subcarriers in the OFDM system;

b (n) is a second partial sequence of the training sequence of the transmitting end, which is a conjugate symmetric sequence of the A (n) sequence, i.e.

C (n) is a third part of the sequence of the training sequence of the transmitting end, which is obtained by inverting the even number of the sequence A (n), that is

D (n) is a fourth part of the transmitting end training sequence, which is obtained by inverting the even number of the B (n) sequence, i.e.

(2) Set the length to N_gAdding the cyclic prefix to the front end of the training sequence T of the transmitting end to obtain the cyclic prefix P with the length of N + N_gTraining symbol S ═ P T]And transmitting the training symbol;

(3) at the receiving end, setting the length of a receiving window as N, and constructing a timing metric function M (d) in the window length:

wherein,

the correlation function is represented by a function of the correlation,

representing energy functions, where m, k are intermediate variables of functions P (d), R (d), and d is a variableThe serial number of the sampling point is,

and

respectively receiving samples with different values;

(4) searching the maximum value of the timing metric function M (d) to obtain a timing synchronization estimated value:

completing timing synchronization;

(5) based on timing synchronization estimates

Determining the starting position of the training sequence in the received sample to obtain the training sequence of the receiving end:

wherein,

to receive a sample, n₁N-1, and using the symmetric property of the two sequences before and after the training sequence T', calculating to obtain a rough decimal frequency offset estimation value

(6) Based on timing synchronization estimates

Determining the starting position of the training symbol in the received sample to obtain the training symbol of the receiving end:

wherein,

to receive a sample, n₃＝-N_g,-N_g+ 1.. ang.N-1, and based on a coarse fractional frequency offset estimate

Carrying out rough decimal frequency offset compensation on the training symbol S' to obtain the training symbol S after the first frequency offset compensation₁Further performing fine decimal frequency offset estimation based on the cyclic prefix, and calculating to obtain a fine decimal frequency offset estimation value

(7) According to fine decimal frequency deviation estimated value

Training symbol S after compensating for first frequency offset₁Fine decimal frequency deviation compensation is carried out to obtain a training symbol S after the second frequency deviation compensation₂Then, using the property of integral multiple frequency offset causing shift to the CAZAC sequence, constructing an integral multiple frequency offset decision function F (g):

wherein g is an argument of the function F (), g is 0,1,2,., N-1, p, q are intermediate variables of the function F (g), respectively,

and

respectively taking two receiving samples with different values after secondary frequency offset compensation, and marking the upper marks to represent that conjugation is taken;

(8) searching for a maximum of an integer multiple of the frequency offset decision function F (g)Obtaining an integral multiple frequency offset estimation value:

(9) using rough fractional frequency offset estimation

Fine fractional frequency offset estimation

And integer multiple frequency offset estimation

Obtaining a frequency offset estimation value:

frequency synchronization is completed.

2. The method according to claim 1, wherein the CAZAC sequence in (1) is represented as follows:

wherein N is₁Is the period of CAZAC sequence, takes an even number, and r is N₁Is a reciprocal prime number, v is 0,1₁-1。

3. The method of claim 1, wherein the cyclic prefix P in (2) is N at the tail of training sequence T from the transmitting end_gA data signal.

4. The method of claim 1, wherein (5) a coarse fractional frequency offset estimate is calculated

By the following formula:

wherein, angle () represents taking the phase,

and

two received samples, n, of different values₂0,1, N/2-1, superscript denotes taking the conjugate.

5. The method of claim 1, wherein the coarse fractional frequency offset compensation of the training symbol S 'in (6) is performed by multiplying the training symbol S' by a compensation term

Obtaining a training symbol after the first frequency offset compensation:

6. the method of claim 1, wherein (6) fine fractional frequency offset estimates are calculated

By the following formula:

wherein,

and

two received samples, n, of different values, respectively, after a first frequency offset compensation₄＝0,1,...,N_g-1。

7. The method of claim 1, wherein the training symbol S compensated for the first frequency offset in (7)₁Fine fractional frequency offset compensation is performed on the training symbol S₁By a compensation term

Obtaining a training symbol after the second frequency offset compensation:

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